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SCIENCE ASIA


Volume 47, No. 01, Month FEBRUARY, Year 2021, Pages 106 - 110


On the divisibility fkfx2 + fx + 1

Florian Luca, Prapanpong Pongsriiamb, Laszlo Szalay


Abstract Download PDF

Let F n and Ln be the nth Fibonacci and Lucas numbers, respectively. We show that if Fk j Fx2 + Fx +1, then k 2 f4,7g; if Lk j Fx2 + Fx + 1, then k 2 f2, 4g.


Keywords

Fibonacci number, Lucas number, divisibility, Diophantine equation, factorization



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